\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}
\begin{align}
	        & \dv{t}f-\poisson{f}{H}_f=0                                                                                                 \\
\os\,\,         & \dv{t}f-\pint{f}{\idv{p}\dvc{x}{p}(\idv{x}).\dvc{p}{x}\tcal}+\pint{f}{\idv{x}\dvc{p}{x}(\idv{p}).\dvc{x}{p}\tcal}=0        \\
\os\,\,         & \dv{t}f+\dvc{x}{p}.(f\dvc{p}{x}\tcal)-\dvc{p}{x}.(f\dvc{x}{p}\tcal)=0                                                      \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f+f(\dvc{x}{p}.\dvc{p}{x}\tcal-\dvc{p}{x}.\dvc{x}{p}\tcal)=0 \\
\os\,\,         & \dv{t}f+\dvc{p}{x}\tcal.\dvc{x}{p}f-\dvc{x}{p}\tcal.\dvc{p}{x}f=0                                                          \\
\os\,\,         & \dv{t}f+v.\dvc{x}{p}f+q(v.\dv{x}A^\top).\dvc{p}{x}f=0
\end{align}

